UCLA

This dissertation consists of three chapters that study unobserved heterogeneity in panel and network data models. In Chapter 1, I propose a semi-nonparametric panel data model with a latent group structure. I assume that individual parameters are heterogeneous across groups but homogeneous within a group while the group membership is unknown. I first approximate the infinite-dimensional function with a sieve expansion; then, I propose a Classifier-Lasso(C-Lasso) procedure to simultaneously identify the individuals’ membership and estimate the group-specific parameters. I show that: (i) the classification exhibits uniform consistency; (ii) C-Lasso and post-Lasso estimators achieve oracle properties so that they are asymptotically equivalent to infeasible estimators as if the group membership is known; and (iii) the estimators are consistent and asymptotically normally distributed. Simulations demonstrate an excellent finite sample performance of this approach in both classification and estimation.

In Chapter 2 (joint with Wenyu Zhou), we study a nonparametric additive panel regression model with grouped heterogeneity. The model can be regarded as a natural extension to the heterogeneous panel model studied in Su, Shi, and Phillips (2016). We propose to estimate the nonparametric components using a sieve-approximation-based Classifier-Lasso method. We establish the asymptotic properties of the estimator and show that they enjoy the so-called oracle property. In addition, we present the decision rule for group classification and establish its consistency. Then, a BIC-type information criterion is developed to determine the group pattern of each nonparametric component. We further investigate the finite sample performance of the estimation method and the information criterion through Monte Carlo simulations. Results show that both work well. Finally, we apply the model and the estimation method to study the demand for cigarettes in the United States using panel data of 46 states from 1963 to 1992.

In Chapter 3, I study a network sample selection model in which 1) bilateral fixed effects enter the pairwise outcome equation additively; 2) link formation depends on latent variables from both sides nonparametrically. I first propose a four-cycle structure to difference out the

fixed effects; next, utilizing the idea proposed in Auerbach (2019), I manage to use the kernel function to control for the selection bias. I then introduce estimators for the parameters of interest and characterize their asymptotic properties.